## Research Seminars in the School of Mathematical Sciences

The School of Mathematical Sciences host regular research seminars delivered by internal and external researchers on topics across mathematical sciences. Seminars take place on the Kevin Street campus and are open to all.

## Seminar 06/11/15: An Examination of the Neural Unreliability Thesis of Autism

An Examination of the Neural Unreliability Thesis of Autism

John Butler

Dublin Institute of Technology

Friday 6 November 2015

1pm, Blue Room, DIT Kevin Street

Abstract:

Reports have recently emerged pointing to the possibility that evoked sensory-neural responses might show greater trial-to-trial variability in individuals on the autism spectrum disorder (ASD). The general notion is that signal averaging procedures typically used in neurophysiological and neuroimaging studies obscure the fact that there are ongoing and presumably relatively dramatic fluctuations in responsiveness to individual events.

Here, we examined this thesis in a matched cohort of typically developing children and children with ASD (N=20), using high-density electrical recordings of visual and somatosensory evoked responses. If the thesis is correct that people with ASD have an unreliable evoked response, a number of straightforward predictions can be made; 1) the averaged evoked response should be broader and have a delayed peak for all components; 2) ASD individuals should have a greater variability of phase dispersion across single trials.

Furthermore, we simulated an unreliable evoked response by introducing temporal and amplitude variability at a single trial level. This simulated data was then compared with the observed TD and ASD data, and illustrated the predictions of the unreliable evoked response and the sensitivity of the measures to small perturbations.

Our data show highly similar reliability in the neural responses to visual and somatosensory stimuli in our matched groups, while the simulated data show differences predicted by the unreliability thesis. These results against a straightforward unreliability hypothesis and instead favours an argument taking into account subtleties and specializations that are present in a complex disorder such as autism.

## Seminar 30/04/15: Quantum Fields and Solid State Physics

Quantum Fields and Solid State Physics

Marianne Leitner

Dublin Institute for Advanced Studies

Thursday 30 April 2015

1pm, Room KA3-011, DIT Kevin Street

## Seminar: 12/02/15: Mathematical Modelling of optical patterning in holographic systems

Mathematical Modelling of optical patterning in holographic systems

Paul O'Reilly

Dublin Institute of Technology

Thursday 12 February 2015

1pm, Room KA3-011, DIT Kevin Street

## Seminar 23/04/15: Robust numerical methods

Robust numerical methods

Eugene O'Riordan

Dublin City University

Thursday 23 April 2015

1pm, Room KA3-011, DIT Kevin Street

## Seminar 11/12/14: Schroedinger operators with slowly decaying Wigner-von Neumann potentials

Schroedinger operators with slowly decaying Wigner-von Neumann potentials

Sergey Simonov

Dublin Institute of Technology

Thursday 11 December 2014

1pm, Room KA3-011, DIT Kevin Street

Abstract:

We consider the Schroedinger operator on the half-line with a periodic background potential and a perturbation which consists of two parts: the slowly decaying Wigner-von Neumann potential csin(2ωx+d)/x^{γ} with γ from (½,1) and a summable part. The continuous spectrum of such an operator has the band-gap structure inherited from the free periodic operator, and in each band of the absolutely continuous spectrum there are two points where the operator can have eigenvalues, because at these points the eigenfunction equation has square summable solutions. These points are called critical. Existence of an embedded eigenvalue is very unstable: it disappears under a change of the boundary condition as well as under a local change of the potential. The talk is devoted to the result that in the generic case of no embedded eigenvalue the spectral density of the operator has a zeroes of the exponential type at the critical points. This extends our earlier result with Sergey Naboko for the case γ=1. In that case zeroes of the spectral density have the power type. Zeroes of the spectral density divide the continuous spectrum into parts and thus can be called pseudogaps.